Bounds on the equation of state from QCD inequalities and lattice QCD

We derive robust bounds on the equation of state (EOS) at finite baryon chemical potential using QCD inequalities and input from recent lattice-QCD calculations of thermodynamic properties of matter at nonzero isospin chemical potential. We use lattice data to deduce an upper bound on the baryon density of the symmetric nuclear matter at a given baryon chemical potential and a lower bound on the pressure as a function of the energy density. We also use constraints from perturbative calculations of the QCD EOS at high density derived in earlier work and causality to delineate robust bounds on the EOS of isospin symmetric matter at densities relevant to heavy-ion collisions.